Wideband 3-D Printed All-Metal Reflectarray With Notches for Low-Cost Millimeter-Wave Applications

In this paper, a 3-D printed all-metal reflectarray is presented for millimeter-wave applications. The array has sub-wavelength element spacing, so that the elements are non-resonant. A two-stage notch is etched at the top of the element, which provides multiple degrees of freedom for phase tuning. The phase variation range is more than 360° by changing the height and width of the first stage of the notch. Thanks to the non-resonant property and the two-stage notching, stable phase shift can be maintained in wide frequency range. A reflectarray with $20\times 20$ elements is fabricated by using 3-D printing technique, which has the merits of flexible construction, light weight and low cost. The simulated and measured results on radiation patterns and realized gain are highly consistent. The measured 1-dB gain bandwidth achieves 17.6%, ranging from 31 GHz to 37 GHz. In the whole 1-dB gain bandwidth, the measured aperture efficiency is higher than 47.7%, with a peak efficiency of 53.6% at 31 GHz. The proposed reflectarray has no substrate loss and can provide high aperture efficiency in wide bandwidth.


I. INTRODUCTION
N OWADAYS, there is a widespread and increasing interest in metaverse, which uses virtual world and virtual objects for entertainment, education, training, and research applications. To support high wireless transmission rate in metaverse, wide bandwidth is needed [1], [2]. Millimeter wave (mm-wave) band is promising for metaverse applications due to its wide bandwidth and small size of devices.
High gain antennas are needed to overcome the drawback of large path loss in mm-wave band [3]. Phased arrays [4], [5], parabolic reflectors [6], [7], and reflectarrays [8], [9] are the typical antenna structures to generate high gain beam. Among them, reflectarray is attractive because it combines the merits of phased arrays and reflectors, which has flexible element configuration and spatial feed simultaneously. Therefore, reflectarrays have low cost, low profile and high efficiency [10]. The elements of the reflectarrays have various types, such as microstrip patch, dipole, slot, dielectric resonant antenna, waveguide. The fabrication of the reflectarray is also flexible, including printed circuit board (PCB) etching, 3-D dielectric or metal printing, and low temperature co-fired ceramic (LTCC) and MEMS micromachining techniques [11], [12], [13], [14], [15].
Microstrip reflectarrays using PCB technique are popular owing to planar structure and ease of fabrication. Various designs have been proposed [16], [17], [18]. However, microstrip reflectarrays have both dielectric loss and conductor loss. The radiation efficiency will decrease when the frequency increases to mm-wave and Terahertz bands [19]. All-dielectric reflectarrays [20], [21], [22] and all-metal reflectarrays [23], [24], [25] are then designed to reduce loss. Metal reflectarray is preferred in applications that have harsh environment due to its mechanical robustness. For example, a metal-only reflectarray is presented in [24]. The 1-dB gain bandwidth is 8.3%. These metal-only designs are similar to microstrip reflectarrays except that the dielectric layer is replaced by air layer. In mm-wave band, it is possible to utilize the 3-D structure, not only the 2-D structure, to develop reflectarray that has high performance. As the wavelength becomes small, the drawback of bulky volume and heavy weight can be ignored. Lots of all-metal reflectarrays have been presented [26], [27], [28], [29], [30], [31], [32], [33], [34]. Waveguide element is one of the most popular 3-D structures [26], [27], [28]. For instance, the first waveguide reflectarray design proposed in 1963 [26]. The reflected phase is shifted by changing the suffers from narrow bandwidth, since the phase shift is highly related to frequency. To increase the bandwidth, non-resonant 3-D structures are proposed, such as metal blocks [26], [27], [28] and grooves [32], [33], [34]. For example, a metal-only reflectarray using metal block is proposed in [29]. The 1-dB gain bandwidth achieves 13.4%.
Recently, 3-D metal printing technique has been introduced in mm-wave antenna designs, which has the merits of low cost and flexible construction ability [35]. In 2016, an all-metal waveguide reflectarray is presented [36]. The metallization of the element is achieved via electroplating. In 2020, a high-gain filtering reflectarray is designed using 3-D printing technique [37]. The aperture efficiency is 40.5%. In [38], a 3-D printed Phoenix cell with wide bandwidth is designed at 20 GHz. The cell consists of a metal block and two concentric waveguides, which leads to very thin walls. It is difficult to scale down the structure to higher frequency regime.
In this paper, a high gain high efficiency metal reflectarray is presented using 3-D metal printing technique. A two-stage notch is etched in each element. The phase shift range is larger than 360 • by changing the depth of the notch. Stable phase response is maintained in wide frequency range. The novelty is summarized as follows. Firstly, the element is nonresonant, which is less sensitive to frequency variation than waveguide. Secondly, the period is sub-wavelength, which has small phase quantization error. Thirdly, the two-stage notch provides multiple freedom to enhance the bandwidth. Finally, the reflectarray is all metal, and is made by 3-D printing, which has low fabrication cost and flexible construction ability.  Fig. 1 shows the geometry of the proposed all-metal element. The size of the element is 4 × 4 mm 2 , corresponding to 0.44 × 0.44 λ 2 0 at 33 GHz. A two-stage notch is etched along x-axis. The depth and width of the notch are optimized to obtain stable phase response in wide frequency band. The element is single linear polarized, whose polarization is along y-axis.

II. UNITS
In order to depict the advantage of the proposed element in phase shift, three types of elements are compared, including metal block, waveguide, and the one-stage notched element. As shown in Fig. 2, the metal block and the notched element have the same size, while the waveguide has the size of 0.68 × 0.34 λ 2 0 . It implies that the waveguide is resonant and operates at TE 10 mode, while the metal block and the notched element are non-resonant. The height of the metal block, the depth of the waveguide and the depth of the notched element are used to change the value of the reflection phase, respectively.
The reflection phases of the three elements are shown at the right part of Fig. 2. All the elements have the same tuning distance of depth or height for fair comparison. As the notched depth or height sweeps from 0 mm to 6 mm, the phase variation of waveguide or block element is small at 25 GHz, but large at 40 GHz. The phase response curves are not parallel under different frequencies. It means that the

FIGURE 3. Evolution from one-stage notch to two-stage notch.
phase of the two types is sensitive to frequency variation, thus the available bandwidth is narrow. On the contrary, in the proposed element, the phase curves are nearly parallel, as the frequency changes. To quantitively evaluate the phase performance of the three types, the data extracted from Fig. 2 is listed in the Table 1. The phase shift range of the notched element keeps around 360 • in the whole frequency band . The properties of sub-wavelength element spacing and two-stage notching lead to a wide band element for reflectarray design.
Based on the one-stage notch, two-stage notch is analyzed to further increase the stability of phase shift in wide frequency band. As shown in Fig. 3, the two notches have the same depth, but the two-stage notch has more parameters to tune the phase response, indicating the potential of wide bandwidth.
The two-stage notch has four parameters (h 1 , h 2 , w 1 , w 2 ) that can be changed. It increases the flexibility of phase tuning, but the optimization process becomes complex. In order to reduce the complexity, the continuous phase shift is dispersed into several discrete states. According to the analysis in [39], the quantization loss caused by 1-bit, 2-bit, and 3-bit discretization is about 3 dB, 0.6 dB, and 0.2 dB, respectively. Take the design complexity, the quantization loss, and the fabrication accuracy into account, 2-bit resolution is adopted to verify the design. Table 2 lists the optimized values of the four states, which correspond to The performances of the one-stage and two-stage notches are compared with 2-bit resolution. Fig. 4 shows the reflection phase difference between any two states. Ideal 90 • or 180 • is subtracted in some curves. For the one-stage notch, the phase difference maintains 90±20 • in the 24-36 GHz band. For the two-stage notch, the phase difference is within 90±20 • in 26-47 GHz band. The relative bandwidth of the two-stage notched element is greatly improved.
Parametric analysis is carried out to analyze the influence of the notch on reflection phase. As shown in Fig. 5, the depth of the notch can change the variation range of the reflection phase curve, especially h 1 . On the other hand, the width of the notch can change the linearity of the reflection phase curve. To be specific, w 1 and w 2 changes the slope of the curve at 33 GHz and 39 GHz, respectively. Therefore, parametric studies reveal that the two-stage notch can effectively tune the phase of the reflection coefficient.
The reflection magnitude of the element in different states is shown in Fig. 6. The reflection magnitude is close to 0 dB in all the states, which means that almost full reflection is achieved. The reason of high efficiency is that the model is made of metal and no dielectric loss exists.
The mechanism of achieving wideband is analyzed. Fig. 7 illustrates the operating principle from the perspective of   multiple reflections [40]. The two-stage notch introduces three reflections at different depths. According to transmission line theory, the input impedance of a transmission line is where Z L is the impedance of the terminal load, Z 0 and h are the characteristic impedance and length of the transmission line, respectively. Z L equals to zero, when the load is shortcircuited. Then, the equation is simplified The reflection coefficient at the input port is From this equation, it is known that the reflection phase is determined by the notched depth. In the proposed element, the model can be viewed as a transmission line with threestage reflections. So the total reflection coefficient ( ) is written as where 1 , 2 , 3 is the reflection amplitude at each stage, which is controlled by the notched width. The element works as a multi-stage impedance transformer. It should have wider bandwidth than the one-stage transformer, because the proposed model has more degrees of freedom for optimization, which has already been indicated in Fig. 4. This is another reason of wideband performance, apart from the sub-wavelength element spacing.
The effect of oblique incidence on phase shift is depicted in Fig. 8. Stable phase response is observed in the frequency band, when the incident angle sweeps from 0 • to 30 • . As the incident angle of the reflectarray is designed to be within 30 • , the phase is little changed under different incident angles.

III. EXPERIMENTAL RESULTS
A reflectarray with 20×20 elements is designed based on the notched element. Standard horn antenna operating at 26.5-40 GHz band is adopted as the feeder, which has the gain of 21.4 dBi at 33 GHz. The feeder is 25 • offset from the z-axis. The ratio of the focal distance to the diameter of the array (F/D) is 2.6, considering the trade-off between illumination efficiency and spillover efficiency.
According to the theory of reflectarray design, the phase of the mn-th element can be calculated as where k 0 is the wavenumber in free space, d mn is the distance between the phase center of the feed and the mn-th element, ϕ req,mn is the required phase when the main beam points to the angle of (ϕ r , θ r ). ϕ is a phase constant that provides an additional degree to optimize the phase distribution of the array, and increases the aperture efficiency.
In the simulation of unit cell, periodic boundary is used, which means that the notched depths of adjacent elements are the same. However, in reflectarray design, the notched depths of adjacent elements are different, since the phase distribution is not uniform. Therefore, one may think that the unit model is not accurate, and some elements are similar to waveguides when the notches are blocked by adjacent elements. In order to eliminate these concerns, the unit model is slightly modified. As shown in Fig. 9, narrow grooves with 0.5mm width (w 3 ) are periodically etched between adjacent elements along the x-direction to isolate the elements, so that all the notches will not be blocked by the neighbor ones. By comparing the results of the two models, it is found that both models have similar reflection behaviors. Therefore, the operating mechanism of the proposed element is different from that of waveguide, and the unit model can be used to analyze the performances of the reflectarray.
The prototype of the proposed reflectarray is fabricated by using low-cost 3-D metal printing technique. Fig. 10 shows the photograph and phase distribution of the reflectarray. 3-D metal printing facility developed by ZRapid Tech Company is employed for the array's fabrication. The axis resolution of the printer is 0.2 mm. The thickness of the layer can be reduced to 0.05 mm by decreasing the printing speed. Aluminum alloy AlSi10Mg powder is chosen as the printing material, due to the small grain size of the spherical metal powder. The diameter of the metal powder is between 15∼53 μm. The cost of the fabrication is less than 100 US dollar. The aperture size of the reflectarray is 80×80 mm 2 (8.8×8.8 λ 2 0 , λ 0 is the wavelength at 33 GHz in free space). A 2.5-mmthick metal base is used to enhance the mechanical strength. This modification has little effect on the performance.
The radiation patterns of the reflectarray are measured in a near-field chamber. Fig. 11 shows the simulated and measured gain and aperture efficiency of the reflectarray. The measured frequency is from 27 GHz to 40 GHz, due to the limitation of the chamber. Good agreement is observed between the simulated and measured data. The measured gain is around 25 dBi. The 1-dB gain bandwidth is about 17.6%, ranging from 31 GHz to 37 GHz. It is observed that both the directivity and the gain increase as the frequency increases. A more accurate evaluation for wideband high gain antenna is using the aperture efficiency, which is calculated as where G is the peak gain, and A p is the physical aperture area of the reflectarray.  Based on this equation, the simulated and measured aperture efficiencies are calculated. As shown in Fig. 11(b), the measured peak aperture efficiency achieves 53.6% at 31 GHz. The aperture efficiency is higher than 47.7% in the whole 1-dB gain bandwidth. The discrepancy between the simulated and measured data is mainly caused by fabrication and measurement errors. Fig. 12 shows the normalized radiation patterns in the xoz and yoz planes at four representative frequency points. It is shown that the simulated and measured radiation patterns agree well. Pencil beam is observed at all the four points. The measured side lobe level (SLL) is below -15 dB at all the frequency points. Slight beam squint is observed when the frequency changes, which can be reduced by optimizing the location of the feeder or using two feeders [41], [42]. Table 3 compares the performances of the proposed antenna with other all-metal reflectarray antennas. Compared with the referenced designs, the proposed reflectarray has wider 1-dB gain bandwidth and higher aperture efficiency. In addition, the fabrication of the proposed prototype is based on 3-D printing technique, thus the cost is low.

IV. CONCLUSION
In this paper, a wideband 3-D printed metal reflectarray is investigated for mm-wave applications. By etching twostage notch in each element, stable reflection phase shift is achieved in wide frequency range. The widths and depths of the notch provide multiple degrees of freedom to optimize the bandwidth. The all-metal reflectarray is fabricated by using 3-D metal printing. The measured 1-dB gain bandwidth covers 31-37 GHz band, and the aperture efficiency is higher than 47.7% in the entire gain bandwidth. The proposed reflectarray has the merits of low cost, wide bandwidth, and high aperture efficiency, which is promising for metaverse applications.